# Thread: mean and standard deviation

1. ## mean and standard deviation

I have scanned over and over a similar problem on the forum, i just cannot understand.
I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
Mean- 1250 Std. dev = 120

(a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

(b) Find Pr(1250 < X < 1380)
= Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
Pr(1250 < X < 1380) = look up z in tables

(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,

2. Hello,

Originally Posted by roxy
I have scanned over and over a similar problem on the forum, i just cannot understand.
I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
Mean- 1250 Std. dev = 120

(a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

(b) Find Pr(1250 < X < 1380)
= Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
Pr(1250 < X < 1380) = look up z in tables

(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,
The z-table is made up for a standard normal distribution..

So for a random variable X that has a normal distribution, a mean of $\displaystyle \mu$ and a standard dev of $\displaystyle \sigma$, there is Z that has a standard normal distribution :

$\displaystyle Z=\frac{X-\mu}{\sigma}$

So transform $\displaystyle P(1250<X<1380)=P \left(\frac{1250-1250}{120}<Z<\frac{1380-1250}{120} \right)$$\displaystyle =P(0<Z<1.083)= \text{look on the table} Same for \displaystyle P(1135<X<1275)=P(-0.9583<Z<0.2083)=P(Z<0.2083)$$\displaystyle -P(-0.9583<Z)$$\displaystyle =P(Z<0.2083)-(1-P(Z<-0.9583))=P(Z<0.2083)+P(Z<-0.9583)-1$

3. Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation
(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,[/quote]

For this one fins the two z-score, then look them up to see what probability corresponds.

$\displaystyle z=\frac{x-{\mu}}{\sigma}$

$\displaystyle -.958=\frac{1135-1250}{120}$

Look up in the table and we get .169

$\displaystyle .208=\frac{1275-1250}{120}$

Look up in the table and we get .582

Subtract and we get a probability of .413

4. Thankyou, i will have a look at all the info you sent. sorry i cant give you chocolates, maybe virtual.

5. ## still stuck

Look up in the table and we get .169

Look up in the table and we get .582

Subtract and we get a probability of .413 _

this .169 and .582 is where i am having trouble. when i look the .958 up in the z tables all i get is .3309 . when i look up z= .208 i find .824